Pythagorean Theorem and its Converse
The Pythagorean Theorem, a fundamental principle in geometry, establishes a relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Its converse, equally significant, asserts that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. These intertwined principles provide crucial insights into the properties and relationships within triangles.
Questions
- The width of a rectangle is 3 feet and the diagonal is 5 feet. What is the area of the rectangle?
- Does it matter which sides you choose for a, b, c in a right triangle, when applying the pythagorean theorem?
- What is the diagonal measurement of a 5' by 3' rectangle?
- Using the Pythagorean Theorem, how do you find the length of side B given that side A = 10 and hypotenuse C = 26?
- Using the pythagorean theorem, how do you solve for the missing side given a = 14 and b = 13?
- One leg of a right triangle is 96 inches. How do you find the hypotenuse and the other leg if the length of the hypotenuse exceeds 2 times the other leg by 4 inches?
- How do you use the Pythagorean Theorem to find the missing side of the triangle given: b = 5, c = 8?
- Hulk left home and walked 8 blocks west. Then he turned and walked 6 blocks north. If each block is 500 ft long, how far is Hulk from home?
- The given lengths are: 24, 30, 6 square root of 41, do they represent the sides of a right triangle?
- How do you find the area of a right triangle with the hypotenuse being 15 and one side being 12?
- How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures given c is the hypotenuse and we have b = 5, c = 8?
- Using the Pythagorean theorem how would you find B if A =12 and c=17?
- The diagonal of a square has length #12sqrt2# ft. How do you find the length of the side of the square?
- In a right triangle, if c = 12 and b = 10, what is the length of a in simplified form?
- A ladder placed 12.5 feet from a building touches a building exactly 30 feet from the ground. What is the length of a ladder?
- Using the pythagorean theorem, how do you solve for the missing side given a = 8 and b = 15?
- The diagonal of the rectangle is 61cm and the width is 11cm. How to you find the length?
- The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?
- Gena is working on her math project. She has trimmed the sides of a square cardboard by 7 decimeters. The area of the cardboard then has decreased by 81 square decimeters. What was the original length of a side of the cardboard?
- Find the value of x?